The original quantity of a radioisotope was 100 mCi. How long will take to reduce to 75 mCi, if the disintegration constant is 0.0479 day ¹?

Q: , (a) Let f(x) = −x²-x. Use definition of the derivative Equation 3.4 to compute f'(x). (No other…

A: The objective of the question is determine the equation of tangent line to the given function.

Q: I. Find the solution set of the following. 2(1 + cos x) sin x 3. tan X 2 x = [0, π] 1.3

A: Solution 1.3 Given, tanx2= 2(1+cosx)sinx,  x∈[0,π]

Q: 4.1 4.2 Calculate the expenses to keep the Zoo open per day. Use a 30 day month. Tickets cost…

A: 4.1 To calculate the expenses to keep the Zoo open per day. To use a 30 day month.4.2 Tickets cost…

Q: How do you indicate an 'or equal to' inequality on a graph for a 2-variable inequality? By using a…

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Q: In addition to 1 and 21, what are the factors of 21? 3 and 6 3 and 7 10 and 11 1 and 20

A: Question: In addition to 1 and 21 , what are the factors of 21 ?

Q: Consider the parabola f(x) = -x² - 4x-7 i) Write the equation in vertex form. ii) Find the vertex…

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Q: 1.0⁰ 7 -2 dy 1+ y² 1 +x³ = π 2x + 3 da is an improper integral 1 - 1 (₂ ² ² ₁ + 2x + 1) dz dx + 1…

A: Given problem:- Which of following  is True? a)  ∫0∞dy1+y2=π b) ∫-2711+x3dx is an improper integral…

Q: car company has $44,000 to spend on robots to put paint on new cars. There are 2 types of robots,…

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Q: Consider the integral (ln(x))6 dx:

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Q: 2. Use Green's theorem to evaluate fe e-x³ dx + (5x + sin(y²)) dy, where C is the circle x² + y² = 4…

A: Please see the below picture for detailed solution.

Q: Consider the plane π : x − 2y + 3z − 1 = 0 and the line l : x = (1 − y)/2 = z + 1.      1.      Find…

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Q: Use the rules for sums of powers of integers to compute the sum. 22 [² j=8

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Q: Evaluate the following antiderivative/indefinite integral: / [(5x² + ² + + 50² + 7) de 36 X x3 k:…

A: Topic:- application of integration

Q: 5. Prove the identity: cot(A + B) cot(A - B) = cot² B - tan² A tan² A cot² B-1

A: We have to prove the identity

Q: What is 30,264,836 times 97,125,356 ?

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Q: Solve the system of equations eie= cose -isin (0) in(e) is the imaginary unit and is the base of the…

A: Given system of equations eiθ=cosθ+isinθe-iθ=cosθ-isinθ

Q: dy dx = 2x2-5vxy = 4y2

A: 2x2-5xy=4y2We have to find the dydx

Q: Find the value of the given limit. lim tan(4x) I I-0 O a) 1/12 Ob) undefined Oco d) 4

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Q: (i) Consider the function f: R\{-2,3} → R defined by 2x³4x²5x - 3 x²-x-6 f(x)= - (a) Prove, using…

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Q: 20. Find curl(F), where F(x, y, z) = xyz¹i+x²zªj + 4x²yz³k. a) (-4xyz³)j + (xz¹)k b) x²yj+xz¹k c)…

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Q: Set-up the double integral that will solve for the volume of the solid in the first octant bounded…

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Q: ● f sec³(x) dx ● ► f sec¹(x) dx • f sec³(x) dx MTH 32

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Q: Find the linear approximation to f(x, y) f(6.11, 4.17) f(6.11, 4.17) = 5, xy at the point (6, 4,…

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Q: (2) Find the integrals: x² 2 • S √36x² dx

A: Given ∫x2 36-x2dx

Q: 3. S (5x-12)dx x3-6x²+8x

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Q: Consider the smooth parametric curve defined by the equations = t (t²-3) { = 3 (t²-3) ¹ where t € R.…

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Q: 3 ¹₁ (4x² + 7x²) dz 1 Find

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Q: If a cup of coffee has temperature 92°C in a room where the ambient air temperature is 23°C, then,…

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Q: On Integration of Rational Fractions. Distinct linear factors Repeated linear factors x+8 7) 2+ 1²²…

A: 6) Given:       x+8x2+x-2=x+8x-1x+2 The partial fraction decomposition is:…

Q: Find the lengths of the functions of x over the given interval. Approximate if necessary. y=e^x on…

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Q: 2. Use the process of implicit differentiation to find given that: 52³² + 3 = 5xy. Apply implicit…

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Q: Given f''(x) = - 36 sin(6x) and f'(0) = 6 and f(0) = 0. Find f(1) = [

A: Given the function f''x=-36 sin6x and f'0=6 and f0=0 use the integration formulas,…

Q: Evaluate lim 00 312 22 جوان این 01 3-1 O The limit does not exist. 00

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Q: Use integration by parts to find the antiderivative of f(x) = ln(x).

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Q: 2 y²dx + xydy = 0

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Q: car rental companies. Cars R Us charges $100 up front, plus 10 cents per mile. Thrifty Car Rentals…

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Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

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Q: Question 19 Consider 7(a), the 3rd degree Taylor polynomial of f(a)= cos(z) centered at a IT Use the…

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Q: : x-2y+3z-1 = 0 and the line 1 : x = Consider the plane 1. Find the point of intersection of and 1.…

A: Given: x-2y+3z-1=0x=1-y2=z+1

Q: Consider the function f(t) = 6 sec²(t) - 6t³. Let F(t) be the antiderivative of f(t) with F(0) = 0.…

A: The given function is: ft=6sec2t-6t3   As we know that; The expression for the antiderivative:…

Q: Find the equation of the tangent line at the point 0, In 3 3 for f(x)=In 3 e²x² 2e +e²x

A: Topic:- application of derivatives

Q: question

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Q: [2 2x log 2x dx

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Q: Which equation represents a valid first step to solving the following system of equations using the…

A: Given,           2x-2y=5 and -4x+5y=11To find : Solve using elimination method.

Q: 1. Explain two different ways to solve for the derivative of s(0) = 200sin cos

A: Topic = Derivative

Q: Two fire-lookout stations are 14 miles apart, with station B directly east of station A. Both…

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Q: ) In the following exercises, use direct substitution to show that each limit leads to the…

A: Given, limx→ 3x2-2x-3x2-9LetL=limx→ 3x2-2x-3x2-9L=limx→ 3x2-3x+x-3x2-32L=limx→…

Q: An object moves with velocity as given in the graph below (in ft/sec). How far did the object travel…

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Q: The pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of a mole of…

A: Here we will use the chain rule i.e., if u and v are function of t with f=uv then…

Q: 2x log 2x dr 1 (x²+6x+5)3/2 dr

A: As we know that; The Power Rule: ∫xndx=xn+1n+1+C   1). The given integral is: I=∫2xlog2xdx Apply the…